If \((2x)^3 = \sqrt{128}\) and \(x =\sqrt[n]{2}\) , what is the value of \(n\)?
The value of n is 8.
8x^3 = sqrt(128) = 8sqrt(2)
x^3 = sqrt(2) = (2)^0.5
So x = (2)^(1/2)(1/3). Thus, n = 6.
